function?[?I1?I2?]?=?KraskovMI（?X?Y?k?varargin?）
%KraskovMI?computes?the?Kraskov?estimator?for?the?mutual?information.
%???1.?Input:?X?Y
%?????????????k:?nearest?neighbour
%?????????????zeroFix?（optional）:?fix?the?negative?estimation?to?0?（default
%?????????????????????????????????false）;
%
%???univariate:?X?Y?（n?x?1）?vector
%???multivariate:?X?Y?（n?x?m）?matrix?（rows=observations
%???columns=variables）
%
%???2.?Output:?I1?I2:?the?two?estimator?of?MI?I（1）?I（2）?（see?Ref.）
%
%?Ref:?Kraskov?Alexander?Harald?St鰃bauer?and?Peter?Grassberger.
%??????“Estimating?mutual?information.“?Physical?review?E?69.6?（2004）:?066138.
%
%?Author:?Paolo?Inglese?
%?Last?revision:?17-05-2015

if?nargin??4
????error（‘Wrong?input?number.‘）;
end
if?nargin?==?3
????zeroFix?=?false;
end
if?nargin?==?4
????if?~islogical（varargin{1}）
????????error（‘zeroFix?must?be?true?or?false‘）;
????else
????????zeroFix?=?varargin{1};
????end
end
????

if?size（X?1）?~=?size（Y?1）
????error（‘X?and?Y?must?contain?the?same?number?of?samples‘）;
end

nObs?=?size（X?1）;

%?compute?distance?between?each?sample?and?its?k-th?nearest?neighbour
dz?=?zeros（nObs?nObs）;
dx?=?zeros（nObs?nObs）;
dy?=?zeros（nObs?nObs）;
for?i?=?1:nObs
????for?j?=?1:nObs
????????dx（ij）?=?sqrt（sum（（X（i?:）?-?X（j?:））.^2））;
????????dy（ij）?=?sqrt（sum（（Y（i?:）?-?Y（j?:））.^2））;
????????dz（ij）?=?max（[dx（i?j）?dy（i?j）]）;
????end
end

%?find?nx（i）?and?ny（i）
Eps?=?zeros（nObs?1）;
Nn?=?zeros（nObs?1）;

nx1?=?zeros（nObs?1）;
ny1?=?zeros（nObs?1）;
nx2?=?zeros（nObs?1）;
ny2?=?zeros（nObs?1）;
for?i?=?1:nObs
????
????dxSample?=?dx（i?:）;
????dxSample（i）?=?[];
????
????dySample?=?dy（i?:）;
????dySample（i）?=?[];
????
????dzSample?=?dz（i?:）;
????dzSample（i）?=?[];
????[EpsSample?NnSample]?=?sort（dzSample?‘ascend‘）;
????Eps（i）?=?EpsSample（k）;
????Nn（i）?=?NnSample（k）;
????
????nx1（i）?=?sum（dxSample?????ny1（i）?=?sum（dySample?????
????nx2（i）?=?sum（dxSample?<=?Eps（i））;
????ny2（i）?=?sum（dySample?<=?Eps（i））;
????
end

%?mutual?information?estimators
I1?=?psi（k）?-?sum（psi（nx1?+?1）?+?psi（ny1?+?1））?/?nObs?+?psi（nObs）;
I2?=?psi（k）?-?1/k?-?sum（psi（nx2）?+?psi（ny2））?/?nObs?+?psi（nObs）;

if?（zeroFix）
????if?I1?????????warning（‘First?estimator?is?negative?->?0‘）;
????????I1?=?0;
????end
????if?I2?????????warning（‘Second?estimator?is?negative?->?0‘）;
????????I2?=?0;
????end
end

end

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

????I.A....??????3678??2010-06-09?15:35??互信息4\mutual?information?.m

?????文件???????1493??2017-04-26?10:07??互信息6\MutualInfo.m

?????文件???????2499??2015-10-29?09:39??KraskovMI5\KraskovMI.m

?????文件???????1034??2006-01-06?11:29??互信息\condentropy.m

?????文件???????1237??2006-01-06?11:29??互信息\condmutualinfo.m

?????文件????????724??2006-01-06?11:29??互信息\demo_mi.m

?????文件????????477??2007-08-23?09:49??互信息\elementmexheader.h

?????文件????????761??2006-01-06?11:29??互信息\entropy.m

?????文件???????1800??2006-01-06?11:29??互信息\estcondentropy.cpp

?????文件??????40960??2006-01-06?11:29??互信息\estcondentropy.dll

?????文件???????8901??2006-01-06?11:29??互信息\estcondentropy.mexglx

?????文件??????54608??2007-08-23?09:49??互信息\estcondentropy.mexmac

?????文件???????1249??2006-01-06?11:29??互信息\estentropy.cpp

?????文件??????40960??2006-01-06?11:29??互信息\estentropy.dll

?????文件???????3449??2008-03-03?08:34??互信息\estentropy.dsp

?????文件????????528??2008-03-03?10:22??互信息\estentropy.dsw

?????文件???????8605??2006-01-06?11:29??互信息\estentropy.mexglx

?????文件??????53908??2007-08-23?09:49??互信息\estentropy.mexmac

?????文件??????33792??2008-03-03?10:22??互信息\estentropy.ncb

?????文件??????49664??2008-03-03?10:22??互信息\estentropy.opt

?????文件???????1286??2008-03-03?09:10??互信息\estentropy.plg

?????文件???????1417??2006-01-06?11:29??互信息\estjointentropy.cpp

?????文件??????40960??2006-01-06?11:29??互信息\estjointentropy.dll

?????文件???????8638??2006-01-06?11:29??互信息\estjointentropy.mexglx

?????文件??????54608??2007-08-23?09:49??互信息\estjointentropy.mexmac

?????文件???????3541??2006-01-06?11:29??互信息\estmutualinfo.cpp

?????文件??????40960??2006-01-06?11:29??互信息\estmutualinfo.dll

?????文件???????9623??2006-01-06?11:29??互信息\estmutualinfo.mexglx

?????文件??????54644??2007-08-23?09:49??互信息\estmutualinfo.mexmac

?????文件???????4754??2006-01-06?11:29??互信息\estpa.cpp

............此處省略97個文件信息